curve #3192

y² + xy = x³ + x² − 2x

a-invariants: [1, 1, 0, -2, 0]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 102
discriminant (Δ): 612
Faltings height: -0.7635
naive height: 14.3874
primes of bad reduction: 2, 3, 17
regulator: 0.1432538929408800714762744130318277199684
submitted by: David Renshaw
submitted at: 2026-09-26 20:41:58 UTC
last updated: 2026-09-26 20:41:58 UTC

Witness: 1 independent point log in to add more points →

(2, 2)

Commentary

Cremona 102a1 = LMFDB 102.a1: https://www.lmfdb.org/EllipticCurve/Q/102/a/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 102, minimal discriminant 612, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:41:58 UTC · history